Finite Group DatabasebetaFinite Group Databasebeta| order | 22784 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | C8×C4⋊C4×C89 ⋊ C2 |
| Sylow | C89 ⋊ #20540 |
906 conjugacy classes of subgroups.
| transitive degree | μt(G) = 11392 |
Polycyclic presentation:
2^8,89|a^2=f,b^2=g,c^2=e,f^2=h,b^a=be,d^a=de,c^b=ce,d^c=dh,i^d=i^883620 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22784, 168333);